Definition

The function $f:K\to\mathbb{R}$ is concave (respectively strictly concave) on $K$ (where $K\subset\mathbb{R}^n$ convex subset) if $-f$ is convex (respectively strictly convex): $f$ concave if $\forall\vec x_1,\vec x_2\in K, \ \lambda\in[0,1]$ $$f(\lambda\vec x_1+(1-\lambda)\vec x_2)\ge\lambda f(\vec x_1)+(1-\lambda)f(\vec x_2)$$ Pasted image 20231101125311.png